IN 

George  Davidson 


Q1  1 


Professor  of  Geography 
University  of  California 


THE  FALLACY 


OF    THE 


SECOND  LAW  OF  THERMODYNAMICS 


AND    THE 


Feasibility  of  Transmuting  Terrestrial 
Heat  Into  Available  Energy 


An  addendum  to  essay  on 
Means  for  Transmuting  Terrestrial  Heat 
into  Available  Energy" 


Read  July  2,  1902,  at  the  Pittsburg  Meeting  of   the  "  Physical  Section' 
of  the  American  Association  for  the  Advancement  of  Science. 


BY 

JACOB  T.  (WAINWRIGHT 

CIVIL  ENGINEER 


CHICAGO 

1902 


,','.: 


Qjif^j^o^ 


PREFACE. 


It  is  hoped  that  the  most  exacting  critic  will  ap- 
preciate that  the  writer  has  herein  succeeded  in 
presenting  this  comparatively  unexplored  subject 
in  a  simple  manner  free  from  all  questions  of  quan- 
tative  analysis  and  unknown  and  doubtful  matter. 


ABSTRACT. 


In  order  to  prove  the  feasibility  of  utilizing  common  omni- 
present terrestrial  heat  as  a  substitute  for  fuel,  it  has  been 
necessary  to  establish  three  new  and  important  truths  or  advance- 
ments in  the  Science  of  Thermodynamics  :— 

FIRST: — Refutation,  or  destruction  of  the  Second  Law  of 
Thermodynamics. 

SECOND: — Establishment  of  a  new  Thermodynamic  principle. 

THIRD  : — Applying  this  new  principle,  so  as  to  dispense 
with  the  external  refrigerating  medium  which  has 
heretofore  been  indispensable  to  the  operation  of 
all  motive  power  heat  engines- 


THE   FALLACY 

OF  THE 


Second  Law  of  Thermodynamics 


AND   THE 


Feasibility  of  Transmuting  Terrestrial 
Heat  Into  Available  Energy 


The  Second  Law  of  Thermodynamics  was  promulgated  by 
Sadi  Carnot,  in  the  year  1824:.  Was  mathematically  established 
by  Professors  Clausius  and  Thompson  (Lord  Kelvin),  independ- 
ently by  each,  respectively  in  the  years  1850  and  1851,  on  the 
same  peculiar  foundation  (on  laws  which  are  now  obsolete)  and  at 
a  date  when  the  laws  of  Boyle,  Gay-Lussac,  and  Watt  were  con- 
sidered sufficiently  accurate  and  applicable  to  all  fluids  within 
practical  limits  of  temperature  and  pressure.  And  both  investi- 
gators were  particular  to  explain  that  the  mathematical  treatment 
and  conclusions  therefrom  were  based  upon  this  assumption,  which 
was  only  approximately  correct  at  best,  and  applied  only  to 
limits  of  pressure  and  temperature  that  were  then  considered 
practicable;  (Memoirs  by  Carnot,  Clausius,  and  Thompson) 
(Translation  by  Professor  Magie,  of  Princeton  University;  Har- 
per &  Bros.,  Publishers,  New  York,  1899). 

Subsequently  (in  the  year  1881),  Professor  Amagat  demon- 
strated that  the  laws  of  Boyle  and  Gay-Lussac  are  very  far  from 
being  true  when  the  fluid's  condition  is  near  the  critical-point. 
Also,  recent  progress  in  the  art  of  liquefying  gases  at  low  tem- 
peratures has  demonstrated  that  practical  limits  of  temperature 
and  pressure  have  increased  to  such  an  extent  that  the  critical- 
point  of  many  gases  is  readily  attained.  Consequently  the  Boyle 
and  Gay-Lussac  law  must  be  abandoned,  and  Amagat's  principle 
must  be  substituted.  Thus  the  Thompson  and  Clausius  assump- 
tion is  no  longer  applicable,  and  their  demonstration  is  destroyed. 

Amagat's  demonstration  of  the  impotency  of  the  Boyle  and 
Gay-Lussac  law  has  been  universally  accepted,  but  the  effect  of 
his  demonstration  upon  the  establishment  of  the  Second  Law  of 
Thermodynamics  has  not  before  been  observed. 


2.00 


Atm.  P.  25     50 


100 


125 


150    175 


200 


225     250 


Fig.  6. 

Figure  6  is  an  exact  reproduction  of  a  diagram  of  isother- 
nials  relating  to  carbon-dioxide,  made  by  Amagat  (Annales  de 
Chimie  et  de  Physique,  6e  Serie,  t.  xxix.  1893)  (Translation  by 
Professor  Bams,  of  Brown  University;  Harper  &  Bros,  publish- 
ers, New  York,  1899)  and  is  the  result  of  actual  research.  The 
abscissas  represent  the  pressures  in  atmospheres,  while  the  ordi- 
nates  represent  the  corresponding  values  of  the  product  resulting 
from  multiplying  the  pressure  by  the  corresponding  volume,  oth- 
erwise designated  as  pv. 

The  lowest  isothermal  shown  by  Amagat  corresponds  to  the 
temperature  of  zero  (274  degrees  absolute)  on  the  Centigrade-ther- 
mometer. Above  the  critical-pressure,  and  within  the  limits  of  his 
diagram,  this  isothermal  is  practically  a  straight  line  which,  if  pro- 
longed, passes  through  the  origin  of  ordinates.  This  shows  that, 
within  these  limits  of  pressure,  this  particular  isothermal  has  con- 
stant volume  for  all  degrees  of  pressure.  Consequently,  at  or  near 
this  particular  finite  temperature,  and  within  these  limits  of 
pressure,  this  particular  fluid  (carbon-dioxide)  becomes  «hxnhi1,hj 
incompressible  or  inert,  as  regards  the  influence  of  pressure  alone. 
Thus,  this  tiii]H>rf<iiif  phenomenon  is  placed  beyond  dispute. 


zro. 


ZOO. 


v$ 


/  00. 


-100 


Fig.  7. 

This  phenomenon  does  not  result  as  an  erratic  change  in  the 
condition  of  the  fluid,  but  is  the  result  of  a  series  of  gradual  and 
well  known  changes.  For  the  purpose  of  showing  this  matter  in 
a  more  familiar  way,  I  have  constructed  the  diagram  of  isother- 
mals  shown  by  Figure  7,  from  matter  shown  in  Figure  6.  In 
Figure  7,  the  ordinates  represent  the  pressures  in  atmospheres, 
while  the  abscissas  represent  the  corresponding  volumes. 

The  Second  Law  of  Thermodynamics  has  been  defined  in 
many  different  ways;  all  of  which  are  merely  mathematical  de- 
ductions from  the  fundamental  law  which  defines,  "Difference  of 


1><  in-, ,  ,)  //////  two  Isodiabatics"  as  a  particular  thermal  prop- 
erty of  a  substance,  which  rcimiinx  c<mxf<n<t  for  <iU  f< mj><  r<itnr<  *. 

Also,  "Difference  of  Entropy  between  two  Isodiabatics"  may 
be  defined  as  the  quantity  of  latent-heat  or  heat  absorbed  (or 
given  up)  at  constant  temperature,  ratioed  or  divided  by  the  cor- 
responding absolute-temperature,  and  comprised  between  limits 
defined  by  the  two  particular  isodiabatics  considered. 

Again,  thermodynamic  changes  or  lines  are  said  to  be  isodia- 
batic  to  each  other,  when  they  are  identical  as  regards  tempera- 
ture changes  and  transfer  of  heat. 

Referring  to  Figure  7,  it  will  be  observed  that  such 
"Difference  of  Entropy,"  measured  on  any  isothermal  whose 
temperature  is  appreciably  greater  than  274  degrees  of  absolute- 
temperature,  will  consist  of  a  finite  quantity  of  latent  heat  ratioed 
or  divided  by  a  finite  absolute-temperature,  and  consequently 
there  results  a  finite  value.  Whereas,  if  measured  on  the 
isothermal  corresponding  to  274  degrees  of  absolute-tempera- 
ture; by  reason  of  the  incompressible  or  inert  condition  acquired 
by  the  fluid  at  or  near  this  particular  temperature,  it  will 
consist  of  an  infinitely  small  quantity  of  latent-heat  ratioed  or 
divided  by  the  very  finite  temperature  of  274  degrees,  and  conse- 
quently there  results  a  value  which  is  zero.  Thus,  in  a 
simple  manner;  free  from  all  questions  of  quantative  analysis, 
and  unknown  and  doubtful  matter;  the  Second  Law  of  Thermo- 
dynamics is  disproved,  as  regards  its  application  to  carbon- 
dioxide,  because  this  law  requires  one  finite  value  for  all  tem- 
peratures.""" 

From  the  relation  between  Entropy  and  the  Second  Law  of 
Thermodynamics,  it  will  be  observed  that  such  law  does  not  per- 
mit the  inert  condition  (which  is  identical  with  the  disappearance 
of  that  property  by  which  latent-heat  can  be  developed),  until 
the  fluid  has  been  cooled  to  an  extent  corresponding  to  zero  of 
absolute-temperature.  Whereas,  Amagat,  by  his  research  work 
on  other  gases,  has  conclusively  demonstrated  that  the  properties 
of  carbon-dioxide  are  typical  for  all  fluids.  Consequently,  all 
gases  become  inert  at  some  fin  <f<  absolute-temperature,  and  there- 
fore the  Second  Law  of  Thermodynamics  is  fallacious  for  all 
fluids. 

After  having  disposed  of  the  Second  Law  of  Thermodynam- 
ics, my  next  object  is  to  establish  the  principle  that,  it  is  possible, 
in  a  j"  /.A'/  thermodynamic  engine,  to  change  or  transform  the 
pressure  condition  or  tension  of  the  working  fluid;  without  trans- 


f  err  ing  heat  to,  or  from  an  external  medium;  without  transferring 
dynamic  energy  to,  or  from  an  external  source;  and  without  re- 
sulting a  changed  temperature. 

My  principle   indirectly  conflicts   with  the   Second   Law  of 
Thermodynamics,  as  will  appear  hereinafter. 


Seal,./   Volume. 


Figures  1,  2,  3,  and  4  show  successive  operations  of  an  ideal 
type  of  transforming  engine. 

A  and  B  are  insulated  cylinders;  each  closed  by  its  respect- 
ive piston;  and  separated,  one  from  the  other  by  the  diaphraui 
D  capable  of  a  perfect  conduction  of  heat. 

The  cylinder  A  contains  the  gas  to  be  treated  or  transformed 
as  regards  its  tension,  the  gas  in  the  cylinder  B  is  merely  :i 
working  fluid.  By  reason  of  the  diaphram  D,  these  separated 
gases  always  have  a  common  temperature. 

Figure  5  is  a  Clapeyron  diagram  showing  the  successive 
operations  in  the  respective  cylinders. 

Figure  1  shows  the  beginning  of  the  operation.  Starting 
with  the  gas  in  the  cylinder  A,  in  the  condition  at  a  on  the  dia- 
gram; and  with  the  gas  in  the  cylinder  B,  in  the  condition  shown 
at  e\  each  gas  having  the  same  temperature  but  differing  as  re- 
gards pressure  and  density. 


The  first  operation  consists  in  densifying  the  gas  in  cylinder 
A,  through  a  falling  range  of  temperature;  and  at  constant  pres- 
sure somewhat  above,  or  at  the  critical  pressure;  until  the  inert 
condition  is  reached.  At  the  same  time,  the  gas  in  cylinder  B  is 
expanded  at  a  sufficient  rate  to  maintain  the  above  mentioned 
constant  pressure  in  cylinder  A  by  reason  of  a  transfer  of  heat 
through  the  diaphram  D.  Figure  2  shows  the  position  of  the 
pistons  at  the  close  of  this  operation,  and  the  points  I  and /on 
the  diagram  show  the  respective  condition  of  these  separated 
gases  after  having  thus  passed  through  the  series  of  conditions 
shown  respectively  by  the  lines  a-~b  and  e-f.  By  reason  of 
Amagat's  principle,  the  gas  in  cylinder  A  has  now  acquired  an 
incompressible  condition,  as  regards  the  influence  of  pressure 
alone. 

The  second  operation  consists  in  applying  an  increased  pres- 
sure on  the  fluid  in  cylinder  A,  while  the  condition  of  the  gas  in 
the  cylinder  B  is  maintained  without  change.  Figure  3  shows 
the  unchanged  position  of  the  pistons  at  the  close  of  this  opera- 
tion, and  the  points  c  and  /  on  the  diagram  show  the  respective 
condition  of  the  separated  gases  after  the  gas  in  cylinder  A  has 
thus  passed  through  the  series  of  conditions  shown  by  the  line 
'ta?,  while  the  condition  of  the  gas  in  cylinder  B  remains 
unchanged. 

The  third  operation  consists  in  densifying  the  gas  in  the 
cylinder  B,  through  a  series  of  conditions  exactly  the  reverse  of 
that  by  which  it  was  expanded;  at  the  same  time,  the  gas  in 
cylinder  A  is  expanded  through  a  range  of  increasing  tempera- 
tures and  a  series  of  pressures  suited  to  maintain  the  gas  in 
cylinder  B  through  its  return  series  of  conditions,  or  in  other 
words,  expanded  on  the  line  <•-<!  which  is  isodiabatic  to  the  line 
a-ft.  Figure  4  shows  the  position  of  the  pistons  at  the  close  of  this 
operation,  and  the  points  d  and  e  on  the  diagram  show  the 
respective  condition  of  the  separated  gases  after  having  thus 
passed  through  the  series  of  conditions  shown  respectively  by  the 
lines  c-d  &u<lf-e. 

These  three  operations  cause  the  transformation  of  the  gas 
in  cylinder  A,  from  the  condition  of  tension  shown  at  ^,  to  the 
increased  tension  shown  at  d;  also  cause  both  gases  to  return  to 
their  initial  condition  as  regards  temperature.  Whereas,  the  gas 
in  cylinder  B  is  caused  to  depart  from  and  return  to  its  initial 

10 


condition  in  all  respects;  depart  and  return  through  one  range  or 
path  of  conditions;  and  consequently  without  a  transfer  of 
heat  through  the  diaphram  D,  in  an  aggregate  sense,  or  in  other 
words,  the  heat  transferred  from  cylinder  A  is  returned  to  it 
again. 

Since  this  change  has  been  effected  by  a  return  to  the  initial 
condition  of  temperature,  and  without  an  aggregate  transfer  of 
heat  through  the  diaphram  D;  it  necessarily  results  that,  in  an 
aggregate  sense,  neither  heat  nor  dynamic  energy  has  been 
transferred  to,  or  from  either  cylinder. 

The  isothermal  a-d  can  be  chosen  at  sufficient  temperature 
to  insure  that,  within  the  limits  of  the  diagram,  it  is  practically 
governed  by  the  law  of  Boyle  and  Gay-Lussac.  In  such  case, 
the  return  of  the  treated  gas  to  its  initial  temperature  means  a 
return  to  its  initial  condition  as  regards  conserved  energy;  and 
consequently,  in  order  not  to  conflict  with  the  First  law  of  Ther- 
modynamics, the  area  a-b-g-n  which  represents  the  external  work 
accompanying  the  compression,  must  be  equal  to  the  area  c-d-m-g 
which  represents  the  external  work  accompanying  the  expansion; 
from  which  it  results  that,  the  point  d  must  be  at  a  higher  pres- 
sure than  the  point  a. 

After  having  demonstrated  the  truth  of  my  principle,  my 
next  object  is  to  show  how  such  principle  can  be  applied  as  a 
means  for  dispensing  with  a  refrigerating  medium,  in  the  opera- 
tion of  a  perfect  heat  engine. 

Again  referring  to  Figures  1  to  5  inclusive;  a  modification 
of  the  apparatus  may  readily  be  conceived,  by  which  the  trans- 
formed fluid  at  the  condition  corresponding  with  the  point  d,  may 
be  transferred  to  another  cylinder  capable  of  effecting  an 
isothermal-expansion  from  the  condition  at  d  to  the  condition  at 
a  by  means  of  heat  received  from  an  external  source,  and  then 
returning  the  fluid  to  the  transforming  engine  to  there  be  trans- 
formed to  its  initial  condition  at  d  in  the  manner  just  described. 

Such  operation  constitutes  a  cycle  which  may  be  successively 
repeated.  And  it  will  be  observed  that;  such  cycle  absorbs  heat 
from  an  external  source,  at  a  constant  temperature;  converts  all 
of  this  heat  into  available  dynamic  energy;  and  does  not  dis- 
charge any  heat  to  an  external  source. 

Thus,  is  presented  the  long  sought  feasibility  of  converting 
Terrestrial  Heat  into  Available  Energy. 

11 


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